Revealing mistake: In the beginning when the commissioner is talking to Batman in the batmobile, as the camera shakes, so does the image on the screen indicating a blue or green screened image. (00:03:15)
Revealing mistake: When Batman is doing his little sliding stunt on the dinosaur exhibit when he and Freeze meet at the beginning, it's obvious that he has roller skates on and is on a rail. (00:05:10)
Revealing mistake: In the opening heist at the Gotham Museum of Art, just after we see the large diamond soaring through the air and Batman incapacitating a goon, Robin skates over to a statue to remove its spear to use it as a vaulting pole. When he whacks the spear to remove it from its position, the icicles on the statue wobble, just like fake rubber icicles. (00:08:20)
Revealing mistake: After Arnie freezes Robin, then freezes the doorway, then wipes his hand on the ice to wave goodbye to our hero, you can see that the clear spot is there before he wipes it with his hand. (00:13:50)
Revealing mistake: When Batman puts a frozen Robin in the water, you can easily tell it's a dummy/model of some sort. Obviously it's not Chris O'Donnell, but it hardly looks even remotely real. (00:14:00)
Revealing mistake: When Mr. Freeze knocks out the two guards after being released from the fridge, one of the guards falls against the fridge causing it to wobble. A big heavy fridge like that should not wobble. (00:55:30)
Revealing mistake: When Poison Ivy and Bane take over the street gang's lair, they try to take down Bane by wrapping chains around his arms. As he throws them over his head, one of the thugs still attached to their chain causes Bane to move backwards slightly. Kind of unlikely considering how strong Bane is. (00:57:40)
Revealing mistake: When the police attempt to arrest Mr. Freeze, he makes his escape with his freezing equipment on a cart. As he pushes the cart, the frozen icicles on it move as though they are made of plastic. (01:17:55)
Revealing mistake: When Robin is being pulled underwater by Ivy's plants he surfaces for air and gets pulled under again. It's obvious the film was just rewound. Then when he finaly gets free we see the shot that was rewound was the same shot used when he escapes. Really bad editing. (01:34:50 - 01:36:40)
Revealing mistake: When Freeze is freezing the town, the cop car that crashed into the store has flexible icicles on the driver side door. Also when the city is being defrosted, when the cop comes out of the car, the icicles are very wobbly. (01:38:15 - 01:48:15)
Revealing mistake: When Gotham City is frozen by Mr. Freeze, there is a shot of a telephone box. The icicles on the telephone box wobble as though they are made of plastic. (01:42:15)
Revealing mistake: When Batman places the heaters around the telescope to thaw the ice, the frozen floor moves like plastic when he places the second heater. (01:45:00)
Revealing mistake: After Batman slides and kicks Freeze, there's a protruding lump under his clothes where the safety cable holding him was.
Revealing mistake: At the diamond gala, Batman several times punches a few henchmen of Freeze, but doesn't even touch them at all.
Revealing mistake: When Batman is snagged by Poison Ivy's vines and pulled up to the ceiling, you can see that the sides of his cape are attached to his thighs by black strings, to keep his cape from falling completely down over his head during the shot.
Revealing mistake: In one scene where our heroes are defrosting Gotham city using the sunlight, we see Commissioner Gordon stepping from his car which has been covered in flexible icicles.
Revealing mistake: At the gala, you can notice the stunt double driving the ice truck for Arnie.
Revealing mistake: In the museum, when Robin breaks the door with his bike you can notice that the door is made of foam rubber or similar.
Revealing mistake: When Batman is about to defrost Robin, he is holding a dummy.
Revealing mistake: While Ivy is fighting Batgirl you can see the stunt double replacing Uma Thurman.
Chosen answer: Purely a creative decision, but based on the tone of this question I don't suppose you're honestly after an answer so much as you are just looking for someplace to express your distaste.
Phixius ★
Because Schumacher wanted to base the suits on Greek sculptures hence the nipples. Don't forget Robin's shorts or Batman wearing different colored cowls in the comics, perhaps this was a nod to that.
Rob245